Bayesian Networks: With Examples in R, Second Edition introduces Bayesian networks using a hands-on approach. Simple yet meaningful examples illustrate each step of the modelling process and discuss side-by-side the underlying theory and its application using R code. The examples start from the simplest notions and gradually increase in complexity. In particular, this new edition contains significant new material on topics from modern machine learning practice: dynamic networks, networks with heterogeneous variables, and model validation. The first three chapters explain the whole process of Bayesian network modelling, from structure learning to parameter learning to inference. These chapters cover discrete, Gaussian, and conditional Gaussian Bayesian networks. The following two chapters delve into dynamic networks (to model temporal data) and into networks including arbitrary random variables (using Stan). The book then gives a concise but rigorous treatment of the fundamentals of Bayesian networks and offers an introduction to causal Bayesian networks. It also presents an overview of R packages and other software implementing Bayesian networks. The final chapter evaluates two real-world examples: a landmark causal protein-signaling network published in Science and a probabilistic graphical model for predicting the composition of different body parts. Covering theoretical and practical aspects of Bayesian networks, this book provides you with an introductory overview of the field. It gives you a clear, practical understanding of the key points behind this modelling approach and, at the same time, it makes you familiar with the most relevant packages used to implement real-world analyses in R. The examples covered in the book span several application fields, data-driven models and expert systems, probabilistic and causal perspectives, thus giving you a starting point to work in a variety of scenarios. Online supplementary materials include the data sets and the code used in the book, which will all be made available from https://www.bnlearn.com/book-crc-2ed/
Author(s): Marco Scutari
Edition: 2
Publisher: CRC Press
Year: 2021
Language: English
Pages: 702
Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface to the Second Edition
Preface to the First Edition
1 The Discrete Case: Multinomial Bayesian Networks
1.1 Introductory Example: Train-Use Survey
1.2 Graphical Representation
1.3 Probabilistic Representation
1.4 Estimating the Parameters: Conditional Probability Tables
1.5 Learning the DAG Structure: Tests and Scores
1.5.1 Conditional Independence Tests
1.5.2 Network Scores
1.6 Using Discrete Bayesian Networks
1.6.1 Using the DAG Structure
1.6.2 Using the Conditional Probability Tables
1.6.2.1 Exact Inference
1.6.2.2 Approximate Inference
1.7 Plotting Discrete Bayesian Networks
1.7.1 Plotting DAGs
1.7.2 Plotting Conditional Probability Distributions
1.8 Further Reading
2 The Continuous Case: Gaussian Bayesian Networks
2.1 Introductory Example: Crop Analysis
2.2 Graphical Representation
2.3 Probabilistic Representation
2.4 Estimating the Parameters: Correlation Coefficients
2.5 Learning the DAG Structure: Tests and Scores
2.5.1 Conditional Independence Tests
2.5.2 Network Scores
2.6 Using Gaussian Bayesian Networks
2.6.1 Exact Inference
2.6.2 Approximate Inference
2.7 Plotting Gaussian Bayesian Networks
2.7.1 Plotting DAGs
2.7.2 Plotting Conditional Probability Distributions
2.8 More Properties
2.9 Further Reading
3 The Mixed Case: Conditional Gaussian Bayesian Networks
3.1 Introductory Example: Healthcare Costs
3.2 Graphical and Probabilistic Representation
3.3 Estimating the Parameters: Mixtures of Regressions
3.4 Learning the DAG Structure: Tests and Scores
3.5 Using Conditional Gaussian Bayesian Networks
3.6 Further Reading
4 Time Series: Dynamic Bayesian Networks
4.1 Introductory Example: Domotics
4.2 Graphical Representation
4.3 Probabilistic Representation
4.4 Learning a Dynamic Bayesian Network
4.5 Using Dynamic Bayesian Networks
4.6 Plotting Dynamic Bayesian Networks
4.7 Further Reading
5 More Complex Cases: General Bayesian Networks
5.1 Introductory Example: A&E Waiting Times
5.2 Graphical and Probabilistic Representation
5.3 Building the Model in Stan
5.3.1 Generating Data
5.3.2 Exploring the Variables
5.4 Estimating the Parameters in Stan
5.5 Further Reading
6 Theory and Algorithms for Bayesian Networks
6.1 Conditional Independence and Graphical Separation
6.2 Bayesian Networks
6.3 Markov Blankets
6.4 Moral Graphs
6.5 Bayesian Network Learning
6.5.1 Structure Learning
6.5.1.1 Constraint-Based Algorithms
6.5.1.2 Score-Based Algorithms
6.5.1.3 Hybrid Algorithms
6.5.2 Parameter Learning
6.6 Bayesian Network Inference
6.6.1 Probabilistic Reasoning and Evidence
6.6.2 Algorithms for Belief Updating
6.6.2.1 Exact Inference Algorithms
6.6.2.2 Approximate Inference Algorithms
6.7 Causal Bayesian Networks
6.8 Evaluating a Bayesian Network
6.9 Further Reading
7 Software for Bayesian Networks
7.1 An Overview of R Packages
7.1.1 The deal Package
7.1.2 The catnet Package
7.1.3 The pcalg Package
7.1.4 The abn Package
7.2 Stan and BUGS Software Packages
7.2.1 Stan: A Feature Overview
7.2.2 Inference Based on MCMC Sampling
7.3 Other Software Packages
7.3.1 BayesiaLab
7.3.2 Hugin
7.3.3 GeNIe
8 Real-World Applications of Bayesian Networks
8.1 Learning Protein-Signalling Networks
8.1.1 A Gaussian Bayesian Network
8.1.2 Discretising Gene Expressions
8.1.3 Model Averaging
8.1.4 Choosing the Significance Threshold
8.1.5 Handling Interventional Data
8.1.6 Querying the Network
8.2 Predicting the Body Composition
8.2.1 Aim of the Study
8.2.2 Designing the Predictive Approach
8.2.2.1 Assessing the Quality of a Predictor
8.2.2.2 The Saturated BN
8.2.2.3 Convenient BNs
8.2.3 Looking for Candidate BNs
8.3 Further Reading
A Graph Theory
A.1 Graphs, Nodes and Arcs
A.2 The Structure of a Graph
A.3 Further Reading
B Probability Distributions
B.1 General Features
B.2 Marginal and Conditional Distributions
B.3 Discrete Distributions
B.3.1 Binomial Distribution
B.3.2 Multinomial Distribution
B.3.3 Other Common Distributions
B.3.3.1 Bernoulli Distribution
B.3.3.2 Poisson Distribution
B.4 Continuous Distributions
B.4.1 Normal Distribution
B.4.2 Multivariate Normal Distribution
B.4.3 Other Common Distributions
B.4.3.1 Chi-Square Distribution
B.4.3.2 Student's t Distribution
B.4.3.3 Beta Distribution
B.4.3.4 Dirichlet Distribution
B.5 Conjugate Distributions
B.6 Further Reading
C A Note about Bayesian Networks
C.1 Bayesian Networks and Bayesian Statistics
Glossary
Solutions
Bibliography
Index
